A bipolar junction transistor (BJT) exhibits a very reliable mathematical relationship between its collector current (IC) and its base-emitter voltage (VBE). FIGS. 1A and 1B show that this relationship can be viewed in reciprocal ways. In FIG. 1A, an input signal is applied to an NPN transistor in the form of a voltage VBE across its base-emitter junction. In this connection mode the output is the collector current IC, in essentially the following manner:IC=ISexp(VBE/VT)  Eq. 1VT is the thermal voltage kT/q which is about 26 mV at 300° K, and IS is commonly called the “saturation current”, which is a basic scaling parameter for a BJT and is invariably very much smaller than IC in practical situations. It will be apparent that the transistor may be a PNP type, with appropriate attention to signal polarities, fabricated in any bipolar technology.
In FIG. 1B, the transistor is operated in a reciprocal fashion. Here, the input signal is arranged to be the collector current IC, while the output signal is now the base-emitter voltage which conforms essentially to the following equation (a rearrangement of Eq. 1):VBE=VT log(IC/IS)  Eq. 2where VT and IS have the same meanings as in Eq. 1. Thus, the transistor can be configured and driven to provide either an exponential or a logarithmic response.
In FIG. 1B, a unity-gain current amplification element ensures that Ic is unaffected by the base current of the transistor. This element is usually realized by a simple BJT emitter-follower or a MOS (metal oxide semiconductor) source-follower of appropriate polarity.
One of the earliest practical circuits to utilize this logarithmic property of a BJT to realize a logarithmic amplifier (log amp) is shown in FIG. 2. In this arrangement, which is sometimes referred to as a “transdiode connection” or “Paterson diode,” the base of Q1 is grounded, and the high-gain operational amplifier (op amp) OA1 is configured to force the collector current IC to equal the signal input current IX while maintaining the collector voltage near ground. The output signal voltage, generally named VLOG, is thenVLOG=−VT log(IX/IS)  Eq. 3
It is common to use base-10 logarithms in such applications, in order to characterize the output directly in terms of decibel (dB) changes in the input signal. It is also common to characterize the operation of a log amp in terms of a “slope voltage,” defined as the amount of change in the output for each decade change in the input magnitude, and an “intercept,” which is the value of input at which the extrapolation of the output in Eq. 3 passes through zero. For a current-input, voltage-output log amp, the function is generally stated asVLOG=VY log10(IX/IZ)  Eq. 4where VLOG is the output voltage, IX is the input current, VY is the slope voltage, and IZ is the intercept. From Eq. 3 it is apparent that the log amp of FIG. 2 has a slope voltage VY of −VT and an intercept IZ of IS. For the basic circuit, VY is −26 mV log (10)≈−60 mV at T=300 K.
At any given calibration temperature, the circuit of FIG. 2 can provide a remarkably accurate measure of the logarithm of a fixed-polarity, constant or moderately-rapid varying input current, and the op amp OA1 allows the output to be loaded while preserving accuracy. However, the saturation current IS is an extremely strong function of temperature, while the thermal voltage VT is proportional to absolute temperature (PTAT). Accordingly, further refinements are needed to ensure the calibration is essentially independent of temperature.
FIG. 3 illustrates a prior art elaboration of the Paterson diode connection providing a stable log-intercept through elimination of the temperature dependence of IS. This scheme uses a second transistor Q2, nominally identical to Q1, and a second op amp OA2 configured as a unity-gain buffer (voltage follower) with its output fed back to its inverting (−) input terminal. With this topology the output is the difference of the two base-emitter voltages:
                              V          LOG                =                ⁢                                            -                              V                T                                      ⁢                          log              ⁡                              (                                                      I                    Z                                    /                                      I                    S                                                  )                                              +                                    V              T                        ⁢                          log              ⁡                              (                                                      I                    X                                    /                                      I                    S                                                  )                                                                                  Eq          .                                          ⁢          5                ⁢        a                                                          ⁢                  =                    ⁢                                    V              T                        ⁢                          log              ⁡                              (                                                      I                    X                                    /                                      I                    Z                                                  )                                                                                  Eq          .                                          ⁢          5                ⁢        b                                                          ⁢                  =                    ⁢                                    V              Y                        ⁢                                          log                10                            ⁡                              (                                                      I                    X                                    /                                      I                    Z                                                  )                                                                                  Eq          .                                          ⁢          5                ⁢        c            where the inputs have been swapped to make VLOG turn out positive. Therefore, the uncertain value of IS has been eliminated, and the intercept is now determined by the reference current IZ which, using well-known techniques, can be supplied by an accurate and temperature-stable current source. This scheme offers “log-ratio” operation.
VLOG still has a temperature-dependent slope VT=kT/q, alternatively written VY=(kT/q)log(10). A common circuit solution is shown in FIG. 4. It uses a resistor R1 from the base of Q2 to ground, having a specific positive temperature-coefficient, slightly greater than PTAT; the feedback path around OA2 is completed using a temperature-stable resistor R2.
Although the circuit of FIG. 4 is practical, the need for a special positive temperature-coefficient (TC) resistor is problematic, even in discrete realizations, and especially so for implementation as a monolithic integrated circuit. Breaking from this traditional solution, the prior art circuit of FIG. 5 uses translinear techniques to provide temperature compensation of the slope without the need for a positive-TC resistor. A translinear multiplier cell is used to form the feedback loop, and all resistors can now be temperature-stable. The compensation is achieved by using a PTAT current IT, and a temperature-stable current IR for biasing the two halves of the multiplier cell. This circuit and further refinements thereof are described more fully in U.S. Pat. No. 4,604,532, by the same inventor as the present invention.